Converging evidence has gradually led to a consensus in favor of computational models of behavior implementing continuous information flow and parallel processing between cognitive processing stages. Yet, such models still typically implement a discrete step between the last cognitive processing stage and motor implementation. This discrete step is implemented as a fixed decision bound that activation in the last cognitive stage needs to cross before action can be initiated. Such an implementation is questionable as it cannot account for two important features of behavior. First, it does not allow to select an action while withholding it until the moment is appropriate for executing it. Second, it cannot account for recent evidence that cognition is not confined prior to movement initiation, but consistently leaks into movement. To address these two features, we propose a novel neurocomputational model of cognition-action interactions, namely the unfolding action model (UAM). Crucially, the model implements adaptive information flow between the last cognitive processing stage and motor implementation. We show that such a model addresses the two aforementioned features. Empirically, the UAM accounts for traditional response time data, including positively skewed initiation time distribution, functionally fixed decision bounds and speed-accuracy tradeoffs in button-press experimental designs. Moreover, it accounts for movement times, movement paths, and how they are influenced by cognitive-experimental manipulations. This move should close the current gap between abstract decision making models and behavior observed in natural habitats.